Предмет:
МатематикаАвтор:
анонимСгруппируем слагаемые по два, и вынесем общие множители, и далее преобразуем.
1) (m^3 - m^2 * n) - (m * n^2 - n^3) =
m^2 * (m - n) - n^2 * (m - n) = (m - n) * (m^2 - n^2) =
(m - n) * (m - n) * (m + n).
2) (x^5 - x^2) + (x^ - 1) = x^2 * (x^3 - 1) + (x - 1) =
x^2 * (x - 1) * (x^2 + x + 1) + (x - 1) =
(x - 1) * (x^4 + x^3 + x^2 + 1).
3) Доказать тождество:
(a^4 + b^4) * (a^2 + b^2) * (a + b) * (a - b) = a^8 - b^8
(a^4 + b^4) * (a^2 + b^2) *(a^2 - b^2) =
(a^4 + b^4) * (a4 - b^4) = a^8 - b^8. Доказано.
Для доказательства использовали формулу:
(a + b) * (a - b) = a^2 - b^2.
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